A cubic autocatalator chemical reaction model with limit cycle analysis and consistency preserving discretization
Qamar Din, Muhammad Shabir, Muhammad Asif Khan
Abstract
This article deals with the study of some qualitative properties of a cubic autocatalator chemical reaction model. Particularly, we obtain a dynamically consistent cubic autocatalator discrete-time model by applying a nonstandard difference scheme. Analysis of the existence of equilibria and their stability is carried out. It is proved that a continuous system undergoes the Hopf bifurcation at its interior equilibrium, whereas the discrete-time version undergoes Neimark-Sacker bifurcation at its interior fixed point. Moreover, numerical simulation is provided to strengthen our theoretical discussion.
Topics & Concepts
DiscretizationMathematicsLimit (mathematics)BifurcationConsistency (knowledge bases)Limit cycleHopf bifurcationStability (learning theory)Applied mathematicsQualitative analysisEquilibrium pointFixed pointBifurcation theoryComputer simulationMathematical analysisDiscrete mathematicsPhysicsComputer scienceNonlinear systemStatisticsDifferential equationSocial scienceQualitative researchSociologyMachine learningQuantum mechanicsNonlinear Dynamics and Pattern FormationAdvanced Thermodynamics and Statistical Mechanicsthermodynamics and calorimetric analyses